SOLUTION: Hi, I am hoping you could solve this equation with a step by step picture on how you got what you did at each step. I have an exam and I am really struggling. Thanks Numerator:

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Question 1110967: Hi, I am hoping you could solve this equation with a step by step picture on how you got what you did at each step. I have an exam and I am really struggling. Thanks
Numerator: 3+3^(1/3)
Denominator: 9^(1/3)
It is actually the cubed root of 3 and the cubed root of 9, I just didnt know how to type that
Found 2 solutions by Alan3354, math_helper:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Numerator: 3+3^(1/3)
Denominator: 9^(1/3)
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It's not an equation. There's no equal sign.
It's a fraction than can be simplified some.
It's "cube root" not cubed root.
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The rendering on this site makes it hard to read. = --- Multiply NUM and DEN by 3^(1/3) = --- =

Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website!
I think this is what you want: (you can use 'show source' to see how to format):

This is not an equation, it is an expression. The question must be to rationalize the expression (get rid of as many roots as possible, in particular, from the denominator):

Multiply top and bottom by
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Simplify denominator:
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Notice that
Multiply out the numerator, using the above equivalence:
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Factor out a 3 from the numerator and cancel it with one of the 3's in the denominator
9=3*3 so now the denominator is just 3: ( 3*Numerator / 9 = Numerator / 3 )
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Expand the contents of the radical signs
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In many cases, this is considered rationalized, and it can be left in this form.

The only additional step I see that might be needed by your teacher would be to
break (A+B)/3 into A/3 + B/3 because it lowers the exponents under the radical sign:
Starting with
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